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Shishya Model Paper 1: SSC Mathematics Part I (Algebra)

Shishya model paper — not official, not leaked

12 questions, 30 marks, about 1 hour, written by Shishya on chapters of the Maharashtra SSC Class 10 Mathematics textbook: Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progression, Financial Planning, Probability, Statistics. It is for revision before term exams (quarterly, half-yearly, mid-term, preparatory or prelim). It is not the board's paper, not a past paper and not a guess at any exam; your school sets its own term-exam portion.

How it was made: the questions and answers were drafted with AI, then every final number was recomputed by a calculator check from the question's own numbers (re-run before each release, last on 27 Oct 2026), and a second, independent AI solve had to reach the same number. Try each question first, then open the worked answer.

  1. Q1

    2 marksLinear Equations in Two Variables

    Solve the pair of linear equations: 2x + 3y = 12 and 3x - 2y = 5. Find the value of x.

    Worked answer
    1. Multiply the first equation by 2 to get 4x + 6y = 24
    2. Multiply the second equation by 3 to get 9x - 6y = 15
    3. Add the two new equations to eliminate y: 13x = 39
    4. Solve for x: x = 39 / 13 = 3

    Answer: x is 3

  2. Q2

    2 marksLinear Equations in Two Variables

    The present age of a father is 4 times the age of his son. After 10 years, the father's age will be twice the age of his son. Find the present age of the father.

    Worked answer
    1. Let the son's present age be x. Then the father's age is 4x.
    2. After 10 years, son's age is x + 10 and father's age is 4x + 10.
    3. According to the condition: 4x + 10 = 2(x + 10)
    4. Expand the right side: 4x + 10 = 2x + 20
    5. Subtract 2x from both sides: 2x + 10 = 20
    6. Subtract 10 from both sides: 2x = 10
    7. Solve for x: x = 5
    8. Calculate father's age: 4x = 4 * 5 = 20

    Answer: 20 years

  3. Q3

    2 marksQuadratic Equations

    Find the product of the roots of the quadratic equation 3x^2 - 5x - 12 = 0.

    Worked answer
    1. a = 3, b = -5, c = -12
    2. Product of roots = c/a
    3. Product = -12/3 = -4

    Answer: The product of the roots is -4.

  4. Q4

    2 marksQuadratic Equations

    Find the value of the discriminant of the quadratic equation 3x^2 + 12x + 9 = 0.

    Worked answer
    1. a = 3, b = 12, c = 9
    2. Discriminant D = b^2 - 4ac
    3. D = 12^2 - 4*3*9
    4. D = 144 - 108
    5. D = 36

    Answer: 36

  5. Q5

    3 marksArithmetic Progression

    The first term of an arithmetic progression is 5 and the common difference is 3. Find the 30th term of the progression.

    Worked answer
    1. a = 5, d = 3, n = 30
    2. a_n = a + (n - 1)d
    3. a_30 = 5 + (30 - 1) * 3
    4. a_30 = 5 + 29 * 3
    5. a_30 = 5 + 87
    6. a_30 = 92

    Answer: The 30th term is 92.

  6. Q6

    3 marksArithmetic Progression

    The first term of an arithmetic progression is 2 and the common difference is 4. Find the sum of the first 15 terms of the progression.

    Worked answer
    1. a = 2, d = 4, n = 15
    2. S_n = n/2 * [2a + (n - 1)d]
    3. S_15 = 15/2 * [2 * 2 + (15 - 1) * 4]
    4. S_15 = 7.5 * [4 + 14 * 4]
    5. S_15 = 7.5 * [4 + 56]
    6. S_15 = 7.5 * 60
    7. S_15 = 450

    Answer: The sum of the first 15 terms is 450.

  7. Q7

    3 marksFinancial Planning

    A shopkeeper issued an invoice for a purchase of Rs. 2,500. The GST rate is 18%, split equally into CGST and SGST. Find the total amount to be paid, including both CGST and SGST.

    Worked answer
    1. CGST = 9% of 2500 = 225
    2. SGST = 9% of 2500 = 225
    3. Total GST = 225 + 225 = 450
    4. Total Amount = 2500 + 450 = 2950

    Answer: Rs. 2950

  8. Q8

    3 marksFinancial Planning

    Rahul bought shares worth Rs. 10,000. The brokerage charge is 2% and GST on brokerage is 18%. Find the total amount Rahul paid for the shares, including brokerage and GST on brokerage.

    Worked answer
    1. Brokerage = 2% of 10000 = 200
    2. GST on Brokerage = 18% of 200 = 36
    3. Total Brokerage Cost = 200 + 36 = 236
    4. Total Amount Paid = 10000 + 236 = 10236

    Answer: Rs. 10236

  9. Q9

    2 marksProbability

    A fair die is thrown once. Find the probability that the number obtained is an even number.

    Worked answer
    1. Total outcomes = 6
    2. Favourable outcomes (2, 4, 6) = 3
    3. Probability = 3/6
    4. Probability = 0.5

    Answer: 0.5

  10. Q10

    2 marksProbability

    Two coins are tossed simultaneously. Find the probability of getting at least one head.

    Worked answer
    1. Total outcomes = 4
    2. Favourable outcomes (HH, HT, TH) = 3
    3. Probability = 3/4
    4. Probability = 0.75

    Answer: 0.75

  11. Q11

    3 marksStatistics

    The following table shows the marks obtained by students in a mathematics test and the number of students who obtained those marks. Calculate the mean marks using the direct method. Marks: 10, 20, 30, 40; Number of Students: 5, 10, 15, 10.

    Worked answer
    1. Total students (N) = 5 + 10 + 15 + 10 = 40
    2. Sum of (marks * students) = (10*5) + (20*10) + (30*15) + (40*10) = 50 + 200 + 450 + 400 = 1100
    3. Mean = Sum of (marks * students) / Total students
    4. Mean = 1100 / 40
    5. Mean = 27.5

    Answer: 27.5 marks

  12. Q12

    3 marksStatistics

    A survey was conducted to find the number of books read by students in a month. The table shows the number of books read and the number of students. Find the mean number of books read per student. Books Read: 2, 4, 6, 8; Number of Students: 10, 15, 20, 5.

    Worked answer
    1. Total students (N) = 10 + 15 + 20 + 5 = 50
    2. Sum of (books * students) = (2*10) + (4*15) + (6*20) + (8*5) = 20 + 60 + 120 + 40 = 240
    3. Mean = Sum of (books * students) / Total students
    4. Mean = 240 / 50
    5. Mean = 4.8

    Answer: 4.8 books

Maharashtra SSC 2027: exam dates and papers →Official papers of earlier years →